Question

Fie x,y,z trei numere reale astfel incat x la patrat-(y-z) la patrat=10 la a treia si 2z-2x-2y=-20

Answer 1

deci ai:

x^2-(y-z)^2=10^3
2*(z-x-y) = - 20 => z-x-y= -10 => x+y-z =10 =>x =10 -y+z =10 -(y-z)
cum x=10 -(y-z)  => (y-z)=10-x inlocuim in x^2-(y-z)^2=10^3 =>
=>x^2-(10-x)^2 =10^3 => x^2-100 -x^2+20*x=10^3=>
=>20*x-100=1000 => x-5=50=> x=55
cum (y-z)=10-x=> y-z = 10-55= -45 deci y-z = -45 =>

cum tu ai de aflat x-y+z =>
x-y+z=x-(y-z) = 55 - (-45 ) =55+45=100=10^2